Seminar: Statistical prediction in variables related to energy production.

Summary:
This talk has an industrial motivation that is the nonparametric forecast of electricity demand for the French producer EDF. We then present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant time-scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first method uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with a feature selection technique is then used within classical clustering algorithms to effectively differentiate among high dimensional populations. The second method uses similarity measures between the whole time-scale representations that are based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Finally the practical performance of these methods is illustrated through the daily profiles of the French electricity power demand involved in nonparametric forecasting as well as individual consumers clustering involved in the forecasting by disaggregation of the electricity consumption. The talk is related to joint works with Anestis Antoniadis, Xavier Brossat, Yannig Goude and Jean-Michel Poggi.